Existence of a Model of $o(κ)=κ^{++}$ from Failure of GCH at a Measurable Cardinal
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909445462687744 |
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| author | Watson, Connor |
| author_facet | Watson, Connor |
| contents | It is well-known that the consistency strength of the GCH failing at a measurable cardinal is the existence of a cardinal $κ$ with $o(κ)=κ^{++}$. As the literature does not contain more than a proof sketch of the lower bound of this equiconsistency, we give an expository proof which fills in the details in order to fill this gap in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of a Model of $o(κ)=κ^{++}$ from Failure of GCH at a Measurable Cardinal Watson, Connor Logic 03E35, 03E45, 03E55 It is well-known that the consistency strength of the GCH failing at a measurable cardinal is the existence of a cardinal $κ$ with $o(κ)=κ^{++}$. As the literature does not contain more than a proof sketch of the lower bound of this equiconsistency, we give an expository proof which fills in the details in order to fill this gap in the literature. |
| title | Existence of a Model of $o(κ)=κ^{++}$ from Failure of GCH at a Measurable Cardinal |
| topic | Logic 03E35, 03E45, 03E55 |
| url | https://arxiv.org/abs/2412.17660 |